Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
548 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 131 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#19104759 | C2 | semidirect |
| 2. #23782213 | C2 | semidirect |
| 3. C4×D4×D163 | C2 | semidirect |
| 4. #23781879 | C2 | semidirect |
| 5. #23781878 | C2 | semidirect |
| 6. #23781871 | C2 | semidirect |
| 7. #23781870 | C2 | semidirect |
| 8. #23781857 | C2 | semidirect |
| 9. #23781687 | C2 | semidirect |
| 10. #23781663 | C2 | semidirect |
| 11. #459×C163 | C2 | semidirect |
| 20. #19104735 | C22 | semidirect |
| 21. #19104722 | C22 | semidirect |
| 34. C4⋊(C163⋊C8) | C22 | semidirect |
| 35. Dic163⋊C8 | C22 | semidirect |
| 36. #19104660 | C22 | semidirect |
| 37. #19104658 | C22 | semidirect |
| 38. #19104656 | C22 | semidirect |
| 40. #127×C163 | C22 | semidirect |
| 42. C4⋊C8×C163 | C22 | semidirect |
| 43. #102×C163 | C22 | semidirect |
| 52. D4×D163 | D4 | semidirect |
| 145. C4×C163 | AGL(1,ℤ/8) | semidirect |
| 160. C163 | #3036 | semidirect |
| 170. #459 | D163 | semidirect |
| 183. #127 | C2×D163 | semidirect |
| 200. C4⋊C8 | C2×D163 | semidirect |
| 204. #102 | C2×D163 | semidirect |
| 311. C4 | #19104759 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104759 | 2 |
| #23782213 | 2 |
| C4×D4×D163 | 2 |
| #23781879 | 2 |
| #23781878 | 2 |
| #23781871 | 2 |
| #23781870 | 2 |
| #23781857 | 2 |
| #23781687 | 2 |
| #23781663 | 2 |
| #459×C163 | 2 |
| #3036 | 163 |